Since this conference has been published in RG, I believe that it is subject to comments.

It addresses an old issue such as comparing different MCDM methods using a same problem. The methods are Weighted SUM (WSM), Weighted Product (WPM) and Analytic Hierarchy Process (AHP), and also shows something that is well known; the fact that a comparison most often produces a disagreement between the ranking produced by these methods.

The presentation in excellent, very clear and illustrative. However, I think that it can be improved by eliminating some errors, and misleading concepts. The object of my comments is to help the authors in producing an ameliorated version of the paper if it is published in the future, and also, more important, correct some errors that can mislead practitioners.

Paragraphs in italics are verbatim copies from the original.

1. “The aim of the MCDM methods is to evaluate the alternatives and/or criteria”.

Not in my opinion. The objective of MCDM is to evaluate alternatives subject to a set of criteria, not to also evaluate criteria. To evaluate criteria, you have different methods.

2- “Althoug0h MCDM as a subdiscipline of Operational Research (OR) has a relatively short history of about 48 years, over 70 MCDM techniques have been developed for facilitating the decision-making process”

This is partially incorrect, MCDM methods started in 1940 during the 2nd World War with the invention of Linear Programming (LP), by Leonid Kantorovich, to help the Russian war effort. In 1948 George Dantzig developed the Simplex algorithm, working on Kantorovich’s work. It was and is still extensively used by tens of thousands of entities world-wide, and considered by many the greatest algorithm of the 20th Century.

Since 1991 this can be found as an Excel add-in to solve MCDM problems. Further developments, which as the authors say, are more that 70, can’t compete with LP. This is found in Excel under the ‘Solver’ name, and it produces, if it exists, an optimal solution, not a compromise solution as most methods. The LP structure allows to formulate and solve very complex scenarios as no other method can.

Of course, the reader will ask, why, if LP is so good the other MCDM were crated?

The reason is simple: LP works only with one objective, which nowadays is non-realistic in many cases, and it can’t work either with qualitative criteria, something that are present in greater or lesser degree in most projects.

The SIMUS method, based in LP and that combines with WSM and Outranking, appeared in 2011 and solves these two problems, although it does not produce optimal but compromise solutions, as the other methods.

3. In my opinion Figure 2 of this paper is incorrect, because it looks for an optimization method and that is quite impossible, due to the contradictions that may exist between criteria. That is, we can’t find the greatest benefit and as the same time reach the minimum cost, but a compromise value.

4. “there are some other methods for determination of objective weights of criteria. The Standard Deviation ( SD ), Entropy , Analytical Hierarchy Process ( AHP )”

This statement is partially incorrect, because AHP is a subjective method and then the weights are product of subjectivity, while SD, Entropy and Ratios produce objective weights.

5. Table 1 asserts regarding advantages of AHP “No bias in decision, and not data intensive.”

These assertions are incorrect, since bias is one of the problems that AHP has. Regarding the second, it is not realistic when one considers the amount of pair-wise comparisons required to tackle even a simple problem, let alone if it is necessary for whatever reasons to add or delete criteria and alternatives.

6. Regarding TOPSIS when in the same Table the authors say that “3.Use of Euclidean Distance property’

This is incomplete, because in TOPSIS you can work with more types of distances, and it depends on the DM choice. This creates uncertainty of results, since they can change according to the type of distance that DM selects.

7. The Table also mention as disadvantages that “4. Difficult to understand because it consists of many algorithms”

Other that WSM and WPM, TOPSIS is probably the easiest and most rational MCDM method.

It uses a very simple algorithm. In contrast, the Table does not mention that TOPSIS is also subject to Rank Reversal as many other MCDM methods.

8. The authors propose an interesting example, giving statistical data to be used in WSM and WPM for the initial matrix, and preferences values from AHP.

They use the same weighting for the three methods, derived from AHP. Even so, the rankings are different.

If the mathematical procedures are correct in any of the three methods, and if we use the same weighting, why the rankings are different?

Well, for starters, because AHP is subject to another subjectivity other that that used for quantifying criteria, and that is because the procedure is repeated for the alternatives.

In my opinion, this introduces a bias in WSM and WPM, because they are introducing in them the criteria weights obtained by other method (AHP), and after that, comparing with AHP.

I believe that they should have used objective weights in the three methods

Their results show the following ranking for WSM and WPM:

WSM: P4 – P5 – P3 – P6 – P2 – P1

WPM: P2 – P4 – P5/P6 – P3 – P1

Notice that rankings are different even using the same criteria weights. WSM works with arithmetic averages while WPM works with geometric averages. Probably that is the reason for the different rankings.

This is explained by the authors as “Because, we have set high weight for strike rate criteria and WPM is directly proportional to linear transformation of the raw data with multiplication hypothesis instead of additive hypothesis like WSM”

I have never seen this difference so well and easy explained, and it also shows a weakness in weighting subjectively criteria.

The same weighting is used here.

AHP: P2 – P4 – P5 – P3 – P6 – P1

P5/P6 for WPM means that both have identical scores

The bolded scores mean that they are very close and then they can be interchangeable.

I solved the same example using SIMUS, using data from Table 3, and the result was:

P4 – P2 – P6 – P1 – P5 – P3

However, SIMUS is totally objective. The ranking reflects the result according the information inputted without any subjectivity, while the other three methods show differences because different subjective data It also shows that since WPM and SIMUS are linear, their results are close.

9. In the Conclusions the paper expresses that “The main issue is that to identify proper optimal model for the selection of best alternative in MCDM techniques”

This is incorrect, because there is not an optimal MCDM model.

However, they are right when saying that “Hence, other MCDM methods should be developed to address this limitation”.

It was not my intention to criticize this paper, my effort is only directed to correct some aspects that are incorrect